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Chapter 9: Q. 9.114 (page 953)

Graph f(x)=(x-3)2+1using transformations.

Short Answer

Expert verified

The graph of f(x)=(x-3)2+1is

Step by step solution

01

Step 1. Given data  

The given quadratic function isf(x)=(x-3)2+1

02

Step 2. Determine the horizontal and vertical shift

Comparer the function with f(x)=(x-h)2+k and determine hand k

role="math" localid="1645139630351" f(x)=(x-3)2+1f(x)=(x-h)2+ksoh=3k=1

So 3units horizontal right shift of f(x)=x2will givef(x)=(x-3)2

1unit vertical upward shift off(x)=(x-3)2 will givef(x)=(x-3)2+1

03

Step 3. plot the graph  of the parent function

Plot the graph off(x)=x2

04

Step 4. horizontal shift of the graph

Shift the graph of f(x)=x2to 3 units right to plot f(x)=(x-3)2

05

Step 5. vertical shift of the graph

Shift the graph off(x)=(x-3)2to 1units upward to plot f(x)=(x-3)2+1

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